Does the screen only go blank on normal mode?
If thats the case, try scanning for malware(malicious software may have deleted or corrupted your files that the computer needs to run) in safe mode.
Use free anti-virus programs such as Spybot SD
to scan your computer.
If this does not solve your problem, or you cannot start the computer in safe mode, try using your operating system's (for e.g. Windows XP or Vista) installation disk to repair your computer's files. To do this, just insert the cd into your drive as soon as you turn the computer on and follow the prompts.
I hope your computer will be fixed soon